Optimal Filtering

Optimal Filtering

Optimal filtering is an innovative
technique for detecting a signal against a background of noise or natural
variability. The approach outlined here will investigate optimal filtering in
the spectral regime for two purposes:

To estimate the time required to detect a forced climate signal in
the presence of natural variability.

Application to the construction of a Linear Inverse Model (LIM), and
the eventual use of an LIM to improve the performance of a numerical climate model.

Model natural variability is used to construct spectral EOFs
(based upon covariances between spectral frequencies) from a model
control run. A model can also be used to construct a forced signal
from a forced run. From these the optimal filter can be constructed
and the signal-to-noise ratio for detection can be calculated.
Finally the optimal filter can be applied to observed data to
determine the amplitude of the signal in those data. If there is a detectable
signal in the data, this simultaneously tests the validity of the predicted
signal.